Chapter 6 Practice Test Factor each polynomial completely If

Chapter 6 Practice Test

Factor each polynomial completely. If a polynomial cannot be factored, write “prime.”

If the length is 3 feet more than the width, find the dimensions of the rectangle

Solution

1 a(a+2) -3(a+2) = (a+2)(a-3)

2. x² -x -12 = x² -4x +3x -12 = x(x-4) +3(x-4) = (x-4)(x +3)

3. x² -11x +30 = x² -6x -5x +30 = x(x-6) -5(x -6) = (x-6)(x-5)

4. x² +12x + 36 = x² + 2 *x*6 + (6)² = (x+6)²

^11. The area of the rectangle is 54 sq.ft. Let its width be x ft.. Then its length is x+3 ft so that x(x +3) = 54 or, x² + 3x -54 = 0 or, x² + 9x -6x -54 = 0 or, x(x+9) -6(x +9) = 0 or, (x +9) (x -6) = 0. Now, since x cannot be negative, we have x -6 = 0 or, x = 6. Then x +3 = 9 . Thus the length and the width of the rectangle are 9 ft. and 6 ft. respectively.

12. Let the two numbers be x and y. Then x +y = 14 or, y = 14 -x. Also x² + y² = 100 so that x² +( 14 -x)² = 100 or, x² + 196 - 28x + x² = 100 or, 2x² -28x +96 = 0 or, x² -14x + 48 = 0 or, x² -6x -8x + 48 = 0 or, x(x-6) -8(x -6) = 0 or, (x -6)(x-8) = 0. Thus either x = 8 or x = 6. If x = 8, then y = 14- 8 = 6 and if x = 6, then y = 14-6 = 8. Thus the two numbers are 6 and 8.

13. The height h of a rock t seconds after it is dropped off a cliff is given by the equation 16ht² +400. There appears to be a mistake here. It should probably be h = -16t² +400. Then, when t = 0 , h = 400 so that the height of the cliff is 400. The rock will hit the ground when h = -400. Then, -400 = 16t² +400 or, 16t² = 800 or, t² = 50 so that t = 50 = 52 = 5*1.4142 = 7.07 seconds.

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